22,474 research outputs found
Philosophy and the practice of Bayesian statistics
A substantial school in the philosophy of science identifies Bayesian
inference with inductive inference and even rationality as such, and seems to
be strengthened by the rise and practical success of Bayesian statistics. We
argue that the most successful forms of Bayesian statistics do not actually
support that particular philosophy but rather accord much better with
sophisticated forms of hypothetico-deductivism. We examine the actual role
played by prior distributions in Bayesian models, and the crucial aspects of
model checking and model revision, which fall outside the scope of Bayesian
confirmation theory. We draw on the literature on the consistency of Bayesian
updating and also on our experience of applied work in social science.
Clarity about these matters should benefit not just philosophy of science,
but also statistical practice. At best, the inductivist view has encouraged
researchers to fit and compare models without checking them; at worst,
theorists have actively discouraged practitioners from performing model
checking because it does not fit into their framework.Comment: 36 pages, 5 figures. v2: Fixed typo in caption of figure 1. v3:
Further typo fixes. v4: Revised in response to referee
Literal Perceptual Inference
In this paper, I argue that theories of perception that appeal to Helmholtzâs idea of unconscious inference (âHelmholtzianâ theories) should be taken literally, i.e. that the inferences appealed to in such theories are inferences in the full sense of the term, as employed elsewhere in philosophy and in ordinary discourse.
In the course of the argument, I consider constraints on inference based on the idea that inference is a deliberate acton, and on the idea that inferences depend on the syntactic structure of representations. I argue that inference is a personal-level but sometimes unconscious process that cannot in general be distinguished from association on the basis of the structures of the representations over which itâs defined. I also critique arguments against representationalist interpretations of Helmholtzian theories, and argue against the view that perceptual inference is encapsulated in a module
Convergence Rates of Gaussian ODE Filters
A recently-introduced class of probabilistic (uncertainty-aware) solvers for
ordinary differential equations (ODEs) applies Gaussian (Kalman) filtering to
initial value problems. These methods model the true solution and its first
derivatives \emph{a priori} as a Gauss--Markov process ,
which is then iteratively conditioned on information about . This
article establishes worst-case local convergence rates of order for a
wide range of versions of this Gaussian ODE filter, as well as global
convergence rates of order in the case of and an integrated Brownian
motion prior, and analyses how inaccurate information on coming from
approximate evaluations of affects these rates. Moreover, we show that, in
the globally convergent case, the posterior credible intervals are well
calibrated in the sense that they globally contract at the same rate as the
truncation error. We illustrate these theoretical results by numerical
experiments which might indicate their generalizability to .Comment: 26 pages, 5 figure
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